Fractional conformal invariance method for finding conserved quantities of dynamical systems |
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Institution: | 1. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China;2. College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;3. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China;1. Division of Ocean Science and Technology, Shenzhen Graduate School, Tsinghua University, 518055, Shenzhen, China;2. School of Engineering, Cardiff University, Cardiff CF24 3AA, Wales, UK |
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Abstract: | For a dynamical system that can be transformed into fractional Birkhoffian representation, under a more general kind of fractional infinitesimal transformation of Lie group, we present the fractional conformal invariance method and it is found that, using the new method, we can find a new kind of non-Noether conserved quantity; and we find that, as a special case, an autonomous fractional Birkhoffian system possesses more conserved quantities. Also, as the fractional conformal invariance method’s applications, we, respectively, explore the conformal invariance and conserved quantities of a fractional Lotka biochemical oscillator and a fractional Hojman–Urrutia model. This work constructs a basic theoretical framework of fractional conformal invariance method, and provides a general method for finding conserved quantities of an actual fractional dynamical system that is related to science and engineering. |
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Keywords: | Fractional dynamics Fractional conformal invariance method Conserved quantity Fractional dynamical model |
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